A car weighing 100kg is on a slope that makes an angle 30° with the horizontal. The component of car's weight parallel to the slope is
`(g =10ms^(-2))`

Options

A. 500 N
B. 1000 N
C. 15,000 N
D. 20,000 N

Answer

To solve the problem of finding the component of the car's weight parallel to the slope, we can follow these steps:

### Step 1: Identify the given values
- Mass of the car (m) = 100 kg
- Angle of the slope (θ) = 30°
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Understand the forces acting on the car
The weight of the car (W) can be calculated using the formula:
\[ W = m \cdot g \]
This weight acts vertically downward.

### Step 3: Calculate the weight of the car
Using the values from Step 1:
\[ W = 100 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 1000 \, \text{N} \]

### Step 4: Resolve the weight into components
The weight can be resolved into two components:
1. Component parallel to the slope: \( W_{\parallel} = W \cdot \sin(\theta) \)
2. Component perpendicular to the slope: \( W_{\perpendicular} = W \cdot \cos(\theta) \)

Since we are interested in the component parallel to the slope, we will use the first equation.

### Step 5: Calculate the component of weight parallel to the slope
Substituting the values into the equation:
\[ W_{\parallel} = W \cdot \sin(30°) \]
We know that \( \sin(30°) = \frac{1}{2} \):
\[ W_{\parallel} = 1000 \, \text{N} \cdot \frac{1}{2} = 500 \, \text{N} \]

### Final Answer
The component of the car's weight parallel to the slope is **500 N**.

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